Self-similar fragmentations
Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes
Stochastic flows associated to coalescent processes II : stochastic differential equations
Strong law of large numbers for fragmentation processes
In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than η for 1≥η>0.
Sur les théorèmes de Hewitt-Savage et de de Finetti
Sur l'existence des suites de variables aléatoires s à s indépendantes échangeables ou stationnaires
Survival of homogeneous fragmentation processes with killing
We consider a homogeneous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the decay of the largest fragment for parameter values that allow for survival. In this respect the present paper is also concerned with the probability of extinction of the killed process.